Solve the problem
-The number of mosquitoes $\mathrm { M } ( \mathrm { x } )$, in millions, in a certain area depends on the June rainfall $\mathrm { x }$, in inches: $\mathrm { M } ( \mathrm { x } ) = 2 \mathrm { x } - \mathrm { x } ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?
A) 0 in.
B) 2 in.
C) 1 in.
D) 4 in.

Question

Quizplus · Accepted Answer

The maximum value of $M(x) = 2x - x^2$ can be found by completing the square or using the vertex formula for a parabola. The vertex of a parabola given by $ax^2 + bx + c$ is at $(-b/2a, M(-b/2a))$. Here, $a = -1$ and $b = 2$, so the x-coordinate of the vertex is $-2/(2*(-1)) = 1$. This means the maximum number of mosquitoes occurs at 1 inch of rainfall.

Solve the Problem -The Number of Mosquitoes M(x)\mathrm { M } ( \mathrm { x } )M(x)

Solve the Problem
-The Number of Mosquitoes $\mathrm { M } ( \mathrm { x } )$